Study on on properties and an extension of series and functions obtained from the quantum invariant of rational homology 3-shperes

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400094
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyushu University
• Principal Investigator: TAKATA Toshie 九州大学, 数理学研究院, 准教授 (40253398)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 結び目・３次元多様体の量子不変量

Outline of Final Research Achievements

We obtained a result that the second coefficient is presented by a constant multiple of the square root of the twisted Reidemeister torsion as N goes to the infinity in the asymptotic expansion of N colored Jones polynomial of a 2-bridge knots and SU(2) invariant of some hyperbolic 3-manifolds obtained by surgery along the figure-eight knot, by joint works with T. Ohtsuki.
We verified the slope conjecture for graph knots, i.e. knots whose Gromov volume vanish, by a joint work with K. Motegi.

Free Research Field

低次元トポロジー